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In the causal adjustment setting, variable selection techniques based on either the outcome or treatment allocation model can result in the omission of confounders or the inclusion of spurious variables in the propensity score. We propose a…

Linear model prediction with a large number of potential predictors is both statistically and computationally challenging. The traditional approaches are largely based on shrinkage selection/estimation methods, which are applicable even…

In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of…

Variable selection methods are required in practical statistical modeling, to identify and include only the most relevant predictors, and then improving model interpretability. Such variable selection methods are typically employed in…

To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic…

This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading…

In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…

We propose a new approach for sparse regression and marginal testing, for data with correlated features. Our procedure first clusters the features, and then chooses as the cluster prototype the most informative feature in that cluster. Then…

Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…

In a variety of application areas, there is a growing interest in analyzing high dimensional sparse count data, with sparsity exhibited by an over-abundance of zeros and small non-zero counts. Existing approaches for analyzing multivariate…

This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage…

The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…

This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…

The literature on clustering for continuous data is rich and wide; differently, that one developed for categorical data is still limited. In some cases, the problem is made more difficult by the presence of noise variables/dimensions that…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…